2024/10/23 by Nestor Colin, Colin, Nestor
Mathematics · #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Algebraic Geometry and Number Theory
paper · pdf · doi:10.48550/arxiv.2410.17977
For an odd prime p, we determine the p-primary component of the Farrell cohomology of the pure mapping class groups of a non orientable surface of genus p with k\geqslant 1 marked points. To do this, we classify conjugacy classes of subgroups of order p of the pure mapping class group of a non orientable surface of any genus with marked points. This is obtained by extending the notion of topological equivalence for surface kernel epimorphisms of non Euclidean crystallographic groups, adapting it to the setting of surfaces with marked points.